Answer:
[tex]\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}[/tex]
Step-by-step explanation:
The formula of a volume of a square pyramid:
[tex]V=\dfrac{1}{3}a^2h[/tex]
a - base edge
h - height of a pyramid
We have H = 8in.
Substitute and solve for a:
[tex]\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}[/tex]
